We investigate the stability of a family of self-consistent uniformly rotating collisionless stellar disks by solving the normal mode problem. Every member of the family is unstable. From this family we generate new models that can be either stable or unstable. We give two examples of each. The two unstable models show that nonaxisymmetric modes can still be unstable after all the axisymmetric instabilities have been suppressed. The most troublesome mode appears to be the barlike elliptical deformation.